减去或或乘法 arrays，numpy 广播 它们的形状相同：
>>> np.array(((2,3),(4,5))) - np.array((1,2,3,4))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: operands could not be broadcast together with shapes (2,2) (4,)
>>> np.array((2,3,4,5)) - np.array((1,2,3,4))
array([1, 1, 1, 1])
>>> np.array((2,3,4,5)) - np.array(1)
array([1, 2, 3, 4])
>>> np.array((2,3,4,5)) * np.array(2)
array([ 4, 6, 8, 10])
虽然最后一个操作是有意义的 数学上 （一个 can can multiply a vector 由标量），倒数第二个不是不是（一个不能 添加或减去标量）。
我想知道是否可以告诉Numpy 不 将标量广播到
在加法上下文中的向量或矩阵，升高 value eRror：操作数不能合并在一起。
理由： 乘以数组的每个元素乘以标量，并将标量添加到数组的每个元素中
一个向量是a 向量
space ，即， abelian
小组其元素可以
另外乘以
scalar ，即，一个数字。
IOW，乘以 vector（或矩阵）以一个数字是自然的操作
具有明确定义的属性，例如 distribunitivity ＆amp; c。
但是，在 vector 中添加标量 均未定义。
为什么？！因为您不能在没有指定基础的情况下定义它。
工程师称为 vector （即，数字序列），一个
数学家称为（摘要）向量的坐标表示
具体基础。
当您定义时，
a + [b,c,d,...] := [a+b,a+c,a+d,...]
我看到的是您选择了一个任意向量（巨大的规范！）
y = [1,1,1，...] 并定义
a + X := a*Y + X
，但是为什么选择此特定向量？它比任何其他人都要好吗？
我们都喜欢规范的基础，但是在不同的基础上，这个向量可能会看起来
不同的！
当前的行为可能导致实际错误，例如，如果某人想添加随机错误并写入
my_vector + np.random.normal() # WRONG! each component gets the SAME error!
正确的错误，而不是正确的错误
my_vector + np.random.normal(size=len(my_vector))
，则在处理矩阵时， >是 a
ring
因此，它们 do 具有规范的非0元素 -
10 + array([[1,2],[3,4]])
应该是 array（[[[11,2]，[3,14]]），不是 array（[[[11,12]，[13,14） ]]））！
（出于同样的原因：矩阵只是线性操作员的表示，
它们在不同的基础上看起来不同）。
请注意，单位矩阵在任何基础上都是相同的。
请参阅您可以在矩阵中添加标量吗？以获取2D中的类似说明。
When subtracting or multiplying arrays, numpy broadcasts them to the same shape:
>>> np.array(((2,3),(4,5))) - np.array((1,2,3,4))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: operands could not be broadcast together with shapes (2,2) (4,)
>>> np.array((2,3,4,5)) - np.array((1,2,3,4))
array([1, 1, 1, 1])
>>> np.array((2,3,4,5)) - np.array(1)
array([1, 2, 3, 4])
>>> np.array((2,3,4,5)) * np.array(2)
array([ 4, 6, 8, 10])
while the last operation makes sense mathematically (one can multiply a vector by a scalar), the penultimate one does not (one cannot add or subtract a scalar to a vector).
I wonder if it is possible to tell numpy not to broadcast scalars to
vectors or matrices in additive context, raising ValueError: operands could not be broadcast together instead.
Rationale: the difference between multiplying each element of an array by a scalar, and adding the scalar to each element of the array
A vector is an element of a Vector
space, i.e., an Abelian
group whose elements can
additionally be multiplied by a
scalar, i.e., a number.
IOW, multiplying a vector (or a matrix) by a number is a natural operation
with well defined properties like distributivity &c.
However, adding a scalar to a vector is not defined at all.
Why?! Because you cannot define it without specifying a basis.
What an engineer calls a vector (i.e., a sequence of numbers), a
mathematician calls a coordinate representation of an (abstract) vector in a
specific basis.
IOW, when you define
a + [b,c,d,...] := [a+b,a+c,a+d,...]
what I see is that you have selected an arbitrary vector (of huge norm!)
Y=[1,1,1,...] and defined
a + X := a*Y + X
but why select this specific vector? how is it better than any other one?
We all love the canonical basis, but in a different basis this vector may look
different!
The current behavior can lead to actual errors, e.g., if someone wants to add a random error and writes
my_vector + np.random.normal() # WRONG! each component gets the SAME error!
instead of the correct one
my_vector + np.random.normal(size=len(my_vector))
Also, when dealing with matrices, which are a
ring,
so they do have a canonical non-0 element - the
unit,
the numpy behavior is completely counter-intuitive!
10 + array([[1,2],[3,4]])
should be array([[11,2],[3,14]]), not array([[11,12],[13,14]])!
(for the same reason: matrices are just representations of linear operators, and
they look different in different bases).
Note that the unit matrix is the same in any basis.
Please see Can you add a scalar to a matrix? for a similar explanation in 2d.
发布评论